Q-ANALOG OF IU(N) FOR Q A ROOT OF UNITY

Periodic and partially periodic representations of U(IU(n))q are constructed for q(m) = 1, m being an odd or even integer. The classical non-semisimple IU(n) or U(n)/XI2n algebra has an abelian subalgebra of dimension 2n. Gelfand-Zetlin bases and matrix elements are generalized and adapted to this case. Our previous results for U(IU(n))q for a generic q (not a root of unity) and those for SU(N)q for q(m) = 1 are combined in the present study giving explicit matrix elements and eigenvalues such as the second order Casimir operator D2 = K2 cos(2-pi/m)(h2n+1 + ... + h(nn +1) + n - 1)/cos(2-pi/m). This displays the role of the internal parameters (h(i,n + 1) in the q-analogue of the classical K2 ("mass" squared). The two translation generators (I(n)(n + 1), I(n + 1)(n) become periodic.